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Finite-dimensional approximation of Gaussian processes with linear inequality constraints and noisy observations
No full textInternational audienceDue to their flexibility, Gaussian processes (GPs) have been widely used in non- parametric function estimation. A prior information about the underlying function is often available. In this paper, the finite-dimensional Gaussian approach (Maatouk and Bay, 2017) which can satisfy linear inequality conditions everywhere (e.g. mono- tonicity, convexity and boundary) is considered. In a variety of real-world problems, the observed data usually possess noise. In this paper, this approach has been ex- tended to deal with noisy observations. The mean and the maximum of the posterior distribution are well defined. Additionally, to simulate from the posterior distribu- tion two methods have been used: the exact rejection sampling from the Mode and the Hamiltonian Monte Carlo method which is more efficient in high-dimensional cases. The generalization of the Kimeldorf-Wahba correspondence Kimeldorf and Wahba (1970) is proved in noisy observation cases. A comparison shown that the proposed model outperforms all recent models dealing with the same constraints in terms of predictive accuracy and coverage intervals
An index theorem on asymptotically static spacetimes with compact Cauchy surface
No full textInternational audienceWe consider the Dirac operator on asymptotically static Lorentzian manifolds with an odd-dimensional compact Cauchy surface. We prove that if Atiyah-Patodi-Singer boundary conditions are imposed at infinite times then the Dirac operator is Fredholm. This generalizes a theorem due to Bär-Strohmaier in the case of finite times, and we also show that the corresponding index formula extends to the infinite setting. Furthermore, we demonstrate the existence of a Fredholm inverse which is at the same time a Feynman parametrix in the sense of Duistermaat-Hörmander. The proof combines methods from time-dependent scattering theory with a variant of Egorov's theorem for pseudo-differential hyperbolic systems
Ecrire@LP : collaboration d’enseignants et de chercheurs autour de l’atelier rédactionnel en lycée professionnel
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On decay-surge population models
No full textA paraitre dans: Advances in Applied Probability 55.2International audienceContinuous space-time decay surge population models are those semi-stochastic ones for which deterministically declining populations, bound to fade away, are reinvigorated at random times by bursts or surges of random sizes, resulting in a subtle asymptotic balance. Making use of the notion of scale functions, we exhibit conditions under which such processes either explode or are transient at 0 or at infinity, or recurrent. A description of the structures of both the discrete-time embedded chain and extreme record chain of such continuous-time processes are supplied
Unlocking the sulphur chemistry in intermediate-mass protostars of Cygnus X. Connecting the cold and warm chemistry
No full textInternational audienceContext. The chemistry of sulphur-bearing species in the interstellar medium remains poorly understood, but might play a key role in the chemical evolution of star-forming regions. Aims: Coupling laboratory experiments to observations of sulphur-bearing species in different parts of star-forming regions, we aim to understand the chemical behavior of the sulphur species in cold and warm regions of protostars, and we ultimately hope to connect them. Methods: We performed laboratory experiments in which we tested the reactivity of hydrogen sulfide (H2S) on a cold substrate with hydrogen and/or carbon monoxide (CO) under different physical conditions that allowed us to determine the products from sulphur reactions using a quadrupole mass spectrometer. The laboratory experiments were complemented by observations. We observed two luminous binary sources in the Cygnus-X star-forming complex, Cygnus X-N30 and N12, covering a frequency range of 329-361 GHz at a spatial resolution of 1''5 with the SubMillimeter Array (SMA). This study was complemented by a 3 mm line survey of Cygnus X-N12 covering specific frequency windows in the frequency ranges 72.0-79.8 GHz at a spatial resolution of 34''0-30''0 and 84.2-115.5 GHz at a spatial resolution of 29''0-21''0, with the IRAM-30 m single-dish telescope. Column densities and excitation temperatures were derived under the local thermodynamic equilibrium approximation. Results: We find that OCS is a direct product from H2S reacting with CO and H under cold temperatures (T 2CS, CS, OCS, CCS, C3S, CH3SH, and HSCN). For the hot cores of Cyg X-N12 and N30, only OCS, CS and H2CS were detected. We found a difference in the S-diversity between the hot core and the cold envelope of N12, which is likely due to the sensitivity of the observations toward the hot core of N12. Moreover, based on the hot core analysis of N30, the difference in S-diversity is likely driven by chemical processes rather than the low sensitivity of the observations. Furthermore, we found that the column density ratio of NCS/NSO is also an indicator of the warm (NCS/NSO > 1), cold (NCS/NSO < 1) chemistries within the same source. The line survey and molecular abundances inferred for the sulphur species are similar for protostars N30 and N12 and depends on the protostellar component targeted (i.e., envelope or hot core) rather than on the source itself. However, the spatial distribution of emission toward Cyg X-N30 shows differences compared to N12: toward N12, all molecular emission peaks on the two continuum sources, whereas emission is spatially distributed and shows variations within molecular families (N, O, and C families) toward N30. Moreover, this spatial distribution of all the identified S-species is offset from the N30 continuum peaks. The sulphur-bearing molecules are therefore good tracers to connect the hot and cold chemistry and to provide insight into the type of object that is observed
A history of astronomical optics in France
No full textInternational audienceIn this paper, we explore the advances made in France in astronomical optics. They were quite important in the seventeenth century thanks to Mersenne, Auzout and Picard. Progress in the eighteenth century was less remarkable and many instruments had to be imported from England, but in the following century the developments were again significant thanks in particular to Arago, Foucault, Fizeau, Loewy and the Henry brothers, working with very competent instrument builders. The French school of optics flourished at the end of the nineteenth century and during the twentieth century, thanks to Fabry, his collaborators and successors, as illustrated by Perot, Chrétien, Lyot, Danjon, Paul, Couder, Courtès, Connes, Labeyrie, Baranne and Lemaitre, among others. However, from time to time there was a trend to build instruments that were too original and with little or no future, at the expense of more conventional but better-adapted instruments
Cosmology intertwined: A review of the particle physics, astrophysics, and cosmology associated with the cosmological tensions and anomalies
No full textInternational audienceThe standard Λ Cold Dark Matter (ΛCDM) cosmological model provides a good description of a wide range of astrophysical and cosmological data. However, there are a few big open questions that make the standard model look like an approximation to a more realistic scenario yet to be found. In this paper, we list a few important goals that need to be addressed in the next decade, taking into account the current discordances between the different cosmological probes, such as the disagreement in the value of the Hubble constant H0, the σ8–S8 tension, and other less statistically significant anomalies. While these discordances can still be in part the result of systematic errors, their persistence after several years of accurate analysis strongly hints at cracks in the standard cosmological scenario and the necessity for new physics or generalisations beyond the standard model. In this paper, we focus on the 5.0σ tension between the Planck CMB estimate of the Hubble constant H0 and the SH0ES collaboration measurements. After showing the H0 evaluations made from different teams using different methods and geometric calibrations, we list a few interesting new physics models that could alleviate this tension and discuss how the next decade's experiments will be crucial. Moreover, we focus on the tension of the Planck CMB data with weak lensing measurements and redshift surveys, about the value of the matter energy density Ωm, and the amplitude or rate of the growth of structure (σ8,fσ8). We list a few interesting models proposed for alleviating this tension, and we discuss the importance of trying to fit a full array of data with a single model and not just one parameter at a time. Additionally, we present a wide range of other less discussed anomalies at a statistical significance level lower than the H0–S8 tensions which may also constitute hints towards new physics, and we discuss possible generic theoretical approaches that can collectively explain the non-standard nature of these signals. Finally, we give an overview of upgraded experiments and next-generation space missions and facilities on Earth that will be of crucial importance to address all these open questions
À l’ère de la mondialisation, le rôle nécessaire de la phraséoculture en didactique des langues-cultures en LE
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Single-shot transverse coherence in seeded and unseeded free-electron lasers: A comparison
No full textInternational audienceThe advent of x-ray free-electron lasers (FELs) drastically enhanced the capabilities of several analytical techniques, for which the degree of transverse (spatial) coherence of the source is essential. FELs can be operated in self-amplified spontaneous emission (SASE) or seeded configurations, which rely on a qualitatively different initialization of the amplification process leading to light emission. The degree of transverse coherence of SASE and seeded FELs has been characterized in the past, both experimentally and theoretically. However, a direct experimental comparison between the two regimes in similar operating conditions is missing, as well as an accurate study of the sensitivity of transverse coherence to key working parameters. In this paper, we carry out such a comparison, focusing in particular on the evolution of coherence during the light amplification process